(Sample) Size Matters: Defining Error in Planktic Foraminiferal Isotope Measurement

Abstract:

Planktic foraminifera have been used as carriers of stable isotopic signals since the pioneering work of Urey and Emiliani. In those heady days, instrumental limitations required hundreds of individual foraminiferal tests to return a usable value. This had the fortunate side-effect of smoothing any seasonal to decadal changes within the planktic foram population, which generally turns over monthly, removing that potential noise from each sample. With the advent of more sensitive mass spectrometers, smaller sample sizes have now become standard. This has been a tremendous advantage, allowing longer time series with the same investment of time and energy. Unfortunately, the use of smaller numbers of individuals to generate a data point has lessened the amount of time averaging in the isotopic analysis and decreased precision in paleoceanographic datasets. With fewer individuals per sample, the differences between individual specimens will result in larger variation, and therefore error, and less precise values for each sample. Unfortunately, most workers (the authors included) do not make a habit of reporting the error associated with their sample size. We have created an open-source model in R to quantify the effect of sample sizes under various realistic and highly modifiable parameters (calcification depth, diagenesis in a subset of the population, improper identification, vital effects, mass, etc.). For example, a sample in which only 1 in 10 specimens is diagenetically altered can be off by >0.3‰ δ¹⁸O VPDB or ~1°C. Additionally, and perhaps more importantly, we show that under unrealistically ideal conditions (perfect preservation, etc.) it takes ~5 individuals from the mixed-layer to achieve an error of less than 0.1‰. Including just the unavoidable vital effects inflates that number to ~10 individuals to achieve ~0.1‰. Combining these errors with the typical machine error inherent in mass spectrometers make this a vital consideration moving forward.